What is Refraction Through a Prism?

S6-SA3-0245

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

Refraction through a prism is when light bends as it passes from one medium (like air) into a prism (like glass) and then out again into the first medium (air). This bending happens because light changes speed in different materials, causing its path to shift.

Simple Example

Quick Example

Imagine you are running on a cricket pitch. If you suddenly run from the grass onto a muddy patch, your speed changes, and you might slightly change direction without meaning to. Similarly, when light enters a glass prism from the air, its speed changes, making it bend. It bends again when it leaves the prism and goes back into the air.

Worked Example

Step-by-Step

Let's trace a ray of light entering an equilateral glass prism (angle of prism = 60 degrees) at an angle of incidence of 45 degrees. Assume refractive index of glass is 1.5.

1. **First Refraction (Air to Glass):** Use Snell's Law: n1 * sin(i) = n2 * sin(r1). Here, n1 (air) = 1, n2 (glass) = 1.5, i = 45 degrees.
1 * sin(45) = 1.5 * sin(r1)
0.707 = 1.5 * sin(r1)
sin(r1) = 0.707 / 1.5 = 0.471
r1 = arcsin(0.471) = 28.1 degrees (angle of refraction inside the prism).
---2. **Angle of Prism Relation:** For a prism, A = r1 + r2, where A is the angle of the prism. So, 60 = 28.1 + r2.
r2 = 60 - 28.1 = 31.9 degrees (angle of incidence at the second surface).
---3. **Second Refraction (Glass to Air):** Use Snell's Law again: n2 * sin(r2) = n1 * sin(e). Here, n2 = 1.5, n1 = 1, r2 = 31.9 degrees.
1.5 * sin(31.9) = 1 * sin(e)
1.5 * 0.528 = sin(e)
0.792 = sin(e)
e = arcsin(0.792) = 52.4 degrees (angle of emergence).
---4. **Angle of Deviation:** The total deviation (D) is given by D = i + e - A.
D = 45 + 52.4 - 60
D = 97.4 - 60
D = 37.4 degrees.

**Answer:** The angle of emergence is 52.4 degrees, and the total angle of deviation is 37.4 degrees.

Why It Matters

Understanding refraction through a prism is key to designing optical instruments like binoculars and cameras, which are used everywhere from wildlife photography to security. It's also crucial for developing advanced sensors in AI/ML and medical imaging, helping doctors see inside the human body without surgery. This knowledge helps engineers create better lenses for everything from your smartphone camera to powerful telescopes used by ISRO.

Common Mistakes

MISTAKE: Assuming light always bends towards the normal when entering a denser medium AND away from the normal when leaving. | CORRECTION: Light bends TOWARDS the normal when entering a denser medium (like air to glass) and AWAY from the normal when entering a rarer medium (like glass to air).

MISTAKE: Confusing the angle of incidence with the angle of refraction or emergence. | CORRECTION: The angle of incidence (i) is outside the prism, the angles of refraction (r1, r2) are inside, and the angle of emergence (e) is outside again.

MISTAKE: Forgetting the relationship between the angle of the prism (A), and the internal angles of refraction (r1 and r2): A = r1 + r2. | CORRECTION: Always remember the formula A = r1 + r2 to find unknown internal angles, which is critical for calculating the second refraction.

Practice Questions

Try It Yourself

QUESTION: A ray of light enters a prism from air. If the angle of incidence is 30 degrees and the angle of refraction inside the prism is 19.5 degrees, what is the refractive index of the prism material? | ANSWER: Approximately 1.52 (using Snell's Law: n = sin(i)/sin(r) = sin(30)/sin(19.5) = 0.5/0.333 = 1.50).

QUESTION: An equilateral prism (A=60 degrees) has an angle of incidence of 40 degrees. If the first angle of refraction (r1) is 25 degrees, calculate the angle of incidence at the second surface (r2). | ANSWER: r2 = 35 degrees (using A = r1 + r2, so 60 = 25 + r2).

QUESTION: A ray of light passes through an equilateral glass prism (refractive index 1.5). If the angle of incidence is 48.6 degrees, calculate the angle of emergence and the angle of deviation. (Hint: First find r1, then r2, then e, then D.) | ANSWER: Angle of emergence (e) is approximately 48.6 degrees, and the angle of deviation (D) is approximately 37.2 degrees (This is a case of minimum deviation where i=e).

MCQ

Quick Quiz

What is the primary reason light bends when passing through a prism?

The prism's color changes the light.

Light travels at different speeds in different media.

The prism absorbs some of the light.

The prism's shape forces the light to bend.

The Correct Answer Is:

Light bends because its speed changes when it moves from one medium (like air) to another (like glass in the prism). This change in speed causes a change in direction, which is called refraction.

Real World Connection

In the Real World

You see refraction through a prism in action when a scientist uses a spectrometer to analyze light, like checking the composition of stars, or in a simple 'vIBGYOR' experiment in your school lab. Even in advanced medical endoscopes, tiny prisms are used to guide light and images, helping doctors perform precise surgeries. This concept is also fundamental to how fiber optic cables work, which carry your mobile data and internet across India.

Key Vocabulary

Key Terms

REFRACTION: The bending of light as it passes from one medium to another due to a change in speed. | PRISM: A transparent optical element with flat, polished surfaces that refract light. | ANGLE OF INCIDENCE: The angle between the incident ray and the normal at the surface. | ANGLE OF DEVIATION: The total angle by which the emergent ray has been turned from the direction of the incident ray. | REFRACTIVE INDEX: A measure of how much the speed of light is reduced in a medium compared to its speed in a vacuum.

What's Next

What to Learn Next

Great job understanding how light bends through a prism! Next, you should explore 'Dispersion of Light Through a Prism'. This concept builds directly on refraction and explains why a prism can split white light into its beautiful rainbow of colours, like in a 'VIBGYOR' spectrum. It's super interesting!